Volume 6: The Berlin Years: Writings, 1914-1917 (English translation supplement) Page 420 (432 of 462)

420
DOC. 42 SPECIAL AND GENERAL RELATIVITY
have to be viewed
as 'spatial'
coordinates
and
as a
'time-like' coordinate."
[59]... the
paragraph:
"The second
result,
the curvature
of
light rays
in the
gravitational
field
of
the
sun,
has
already
been
mentioned;
the first
one
refers to the
orbit
of
the
planet Mercury."
[60]... the
following
text: "that
is,
the
equations
of
the
general
theory
of
relativity."
[97]... the fourteenth edition: "Likewise
Perot,
based
on
his
own
observations."
[99]...
was
added: "that is
to
say they are
not convinced
by
the evidence
of
the
existing empirical
material."

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Extracted Text (may have errors)

420
DOC. 42 SPECIAL AND GENERAL RELATIVITY
have to be viewed
as 'spatial'
coordinates
and
as a
'time-like' coordinate."
[59]... the
paragraph:
"The second
result,
the curvature
of
light rays
in the
gravitational
field
of
the
sun,
has
already
been
mentioned;
the first
one
refers to the
orbit
of
the
planet Mercury."
[60]... the
following
text: "that
is,
the
equations
of
the
general
theory
of
relativity."
[97]... the fourteenth edition: "Likewise
Perot,
based
on
his
own
observations."
[99]...
was
added: "that is
to
say they are
not convinced
by
the evidence
of
the
existing empirical
material."

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DOC. 42 SPECIAL AND GENERAL RELATIVITY
419
problem
of
space
in
general
and
on
the
step-by-step
modifications
of
our
ideas about
space
under relativistic
aspects.
I wanted
to show
that
space-time
is not
something
to which
we can
attribute
independent
existence,
disconnected from the
objects proper
of
physical reality. Physical objects
are
not within
space,
but
objects are
rather
spatially
extended.
The
concept
of
'empty space'
thus loses its
meaning."
[15]...
was
appended:
"A
simple
derivation of
the
Lorentz transformation
is
given
in the
appendix."
[26]...
was appended:
"The
general theory
of
relativity suggests
the idea
that
the
electric
mass
of
an
electron is held
together by gravitational
forces."
...
[31]...
was appended:
"See the somewhat
more
elaborate
exposition
in the
appendix."
[37]... final
quotation
marks: "It is the
gravitational
field also that
gives
the
jerk
to the observer."
...
[44]...
was appended:
"The existence
of
the
theoretically
demanded deflection
of
light
has
been
photographically
documented at the solar
eclipse on May 30,
1919,
by
the
English
astronomer
Eddington."
...
[47]...
was appended:
"For the whole
consideration
one
has to
use
the Galilean
(nonrotating)
system
K
as a
reference
body,
because
we
may assume
the
validity
of
the results
of
the
special theory
of
relativity only
with
respect
to K
(relative to
K'
there is
a gravitational
field)."
[49]... in the hand
of
Ilse Einstein: "Note: This
interpretation
has often been
opposed
as
unconvincing
because not
only
the
measuring
rods
but
also the circular
disk would suffer
tangential
contraction. This
argument
is
not
cogent
because the
rotating
disk cannot be viewed
as a
Euclidean
rigid body;
such
body
would shatter
when
brought
to rotation,
according
to
the
postulated
reasons.
In
reality
the disk
plays
no
role in the whole
consideration,
but
only
the system-of rods at
rest
relative
to
each
other-which
rotates
as
a
totality
of
radially
and
tangentially positioned
rodlets."
[55]...
was appended:
"See in
the
appendix.
The
relations
(11a)
and
(12),
which
are
derived there for
coordinates,
apply
also
to
differences
of
coordinates
and,
therefore,
to coordinate differentials
(as
infinitely
small
differences)."
[56]...
by
the
following one:
"This
assignment
need not
even
be such that would

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DOC. 43 COSMOLOGICAL
CONSIDERATIONS
421
Doc.
43
Cosmological
Considerations
in the General
Theory
of
Relativity
This translation
by
W.
Perrett and G. B.
Jeffery
is
reprinted
from H. A. Lorentz
et
al.,
The
Principle
of
Relativity
(Dover, 1952), pp.
175-188.
[1]
IT
is well
known
that
Poisson's
equation
V2£
=
4ttKp
.
. .
.
(1)
in combination with the
equations
of
motion
of
a
material
point
is
not
as yet
a
perfect
substitute
for Newton's
theory
of action at
a
distance. There
is
still to
be
taken into account
the condition
that at
spatial infinity
the
potential
Q
tends
toward
a
fixed
limiting
value.
There
is
an analogous
state
of
things
in the
theory
of
gravitation
in
general
relativity.
Here,
too, we
must
supplement
the
differential
equations
by
limiting
conditions
at
spatial infinity,
if
we really
have to
regard
the universe
as
being
of
infinite
spatial
extent.
[2]
In
my
treatment of
the
planetary problem
I
chose
these
limiting
conditions
in the form
of
the
following assumption:
it
is
possible
to
select
a
system
of reference
so
that at
spatial
infinity
all
the
gravitational potentials
guv
become
constant.
[3]
But
it
is
by
no
means
evident
a
priori
that
we may lay
down
the
same
limiting
conditions
when
we
wish to take
larger
portions
of
the
physical
universe into consideration. In the
following pages
the
reflexions will be
given
which,
up
to the
present,
I
have made
on
this
fundamentally
important
question.
§
1.
The
Newtonian
Theory
It
is well
known that Newton's
limiting
condition
of
the
constant limit for
Q
at
spatial infinity
leads to
the
view
that
the
density
of
matter
becomes
zero
at
infinity.
For
we
imagine
that there
may
be
a place
in universal
space
round
about which the
gravitational
field of matter, viewed
on a
large scale,
possesses
spherical symmetry.
It then
follows
from
Poisson's
equation
that,
in order that
Q
may
tend to
a
177

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